On residual empirical processes of GARCH‐SM models: application to conditional symmetry tests

Naâmane Laïb, Mohamed Lemdani and Elias Ould‐Saïd

Journal of Time Series Analysis, 2008, vol. 29, issue 5, 762-782

Abstract: Abstract. Considering the generalized autoregressive conditionally heteroskedastic with stochastic mean (GARCH‐SM) model, we establish in this article the consistency and the weak representation of a functional of its residual empirical process. Based on this result, a symmetry test for GARCH‐SM model is developed. Simulations are given to show the asymptotic behaviour and normality of the test statistic.

Date: 2008
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https://doi.org/10.1111/j.1467-9892.2008.00580.x

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